In the film I am pretty certain he doesn't have feelings for her that early on. It's only once they live together that something more develops.

In the novel, Evey joins him right after she is attacked and almost raped. She is brought in, not because of feelings but to be groomed as his successor. Him dying and her taking over was all part of his ultimate plan.

In the film, he was attracted to her enough to invite her to his Old Bailey performance, love may have grown later, but his dying words suggest love at first sight.
On the other hand she did not think she wanted him around until he told her he was going to meet his maker, but she was already on the road to forgiving him after seeing evidence that Valerie really existed.

After he asked her to come, she said she should be getting home, and he was quite insistant that "it would be like nothing she had ever seen", if he had no interest in her he would simply have left her to make her own way home.

According to The Oxford Companion to Philosophy, "there is no single defining position that all anarchists hold, beyond their rejection of compulsory government, and those considered anarchists at best share a certain family resemblance".